1. Technical Field
This invention relates generally to games. More particularly, this invention relates to an educational card game for teaching the technique of dimensional analysis.
2. Background
Many math problems encountered in daily life and on scholastic tests involve ratios, a ratio being a value expressed using the word "per." Examples include "miles per hour" or "calories per serving." Some of these problems are familiar and simple. For instance, "If Bill drives 250 miles on 10 gallons of gas, how many miles per gallon did Bill's car get?" Most people know how to divide miles by gallons to get miles per gallon. However, not all problems are so simple. For example, "If a baseball player throws a pitch 15 meters and it takes the ball one second to get to the catcher, what is the speed of the pitch in miles per hour?" Or, "If Tom drives 60 miles per hour and drives 8 hours per day, how many weeks will it take him to drive the 3,000 miles from San Francisco to New York City?"
Dimensional analysis provides a powerful way of solving these types of problems. Essentially, the technique entails multiplying known quantities by dimensional equivalence ratios, a dimensional equivalence ratio being a fraction equal to one, such as "7 days/1 week." Then like units are cancelled from the numerator and denominator of the ratios to arrive at a result with the desired dimensions. For example, applying dimensional analysis to the last problem above, it is apparent that the desired result, or target, units are weeks, because the answer sought is how many weeks it will take Tom to drive the 3,000 miles from San Francisco to New York City. Also, given information includes ratios of 60 miles per hour and 8 hours per day, and that the distance is 3,000 miles. Because none of the given ratios or quantities contain units of weeks, it is apparent that multiplication by a dimensional equivalence ratio involving weeks is necessary. For instance, one week per seven days appears to be a suitable choice here.
Placing the desired target units of weeks on the right side of the equal sign, and placing our first ratio of one week per seven days on the left, the remaining given information ratios are multiplied and appropriately arranged on the left side of the equation so that all the units cancel out, leaving only the desired dimensions of weeks, as shown here: EQU 3,000 miles.times.1 hour/60 miles.times.1 day/8 hours .times.1 week/7 days=0.9 weeks
Thus, it is seen that dimensional analysis can be used to easily solve these types of problems. Unfortunately, dimensional analysis is not taught in most school courses.
The object of the present invention is to teach the fundamentals of dimensional analysis using an educational game. It is a further object of the present invention to teach the fundamentals of dimensional analysis in a way that is entertaining and easy.